Nonlocal Domains Research Articles

An Asymmetry in the Spoken Production of Number Agreement in Second Language English: Adjacency or Locality?

In English, subject-verb agreement is deemed to be ‘local’ if the controller (i.e., the subject) and the target (i.e., the main verb) are adjacent, but ‘non-local’ if these items are separated by one or more terminal nodes. Previous research indicates that second language English learners whose first languages lack subject-verb agreement tend to supply inflection for this functional category less accurately in non-adjacent than adjacent contexts in spoken production. This asymmetry could be driven by either adjacency or locality, since, for subject-verb agreement at least, these two properties are aligned with each other. Phrase-internal agreement, by contrast, is local regardless of whether the controller (i.e., a determiner or quantifier) and the target (i.e., a noun) are adjacent or non-adjacent; hence, for this type of agreement, adjacency and locality are not aligned with each other. In the present study, we gave a sentence-construction task to 64 native speakers of Vietnamese, a language without inflection for number agreement. Suppliance of inflection was lower in non-adjacent than adjacent contexts phrase-internally, and therefore within the local domain itself. We concluded that what gave rise to the asymmetries in inflectional production in our study, and, by extension, also in previous research on subject-verb agreement, was not the distinction between local and non-local domains, but rather the one between adjacent and non-adjacent contexts for agreement. In so doing, we present a more parsimonious analysis of asymmetries in the spoken production of agreement inflection than the one currently available.

A Domain Decomposition Approach for Assessment of Decoupling Capacitors in Practical PDNs

A domain decomposition method is proposed to evaluate the effectiveness of decoupling capacitors in practical power delivery networks (PDNs). The proposed method is based on the separation of a PDN into its local and nonlocal domains. The local domain is constituted by circuit components with the highest impact on the impedance of a specified power pin on a planar PDN. The rest of the PDN makes up the nonlocal domain, which could be of any planar shape. The nonlocal domain is characterized as a distributed circuit, preferably using a numerical electromagnetic (EM) simulator. The self-impedance of the pin depends on the placement configuration of capacitors in its surroundings. Using the pin impedance as a figure of merit, the optimal placement configuration is then sought in the local domain. The impact of the stationary domain is included in calculations as an indefinite impedance and the optimal placement configuration of capacitors is computed using an iterative approach. The proposed method avoids the use of a computationally intensive EM simulation at each iteration step, which significantly speeds up the analysis process.

NONLOCAL SOLUTIONS TO DYNAMIC EQUILIBRIUM MODELS: THE APPROXIMATE STABLE MANIFOLDS APPROACH

This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The approximate solutions are constructed employing the Contraction Mapping Theorem and the fact that the solutions to general equilibrium models converge to a steady state. Under certain nonlocal conditions, the convergence of the approximate solutions to the true solution is proved. We also show that the proposed approach can be treated as a rigorous proof of convergence for the extended path algorithm in a class of nonlinear rational expectation models.

Optimization–Based Coupling of Nonlocal and Local Diffusion Models

ABSTRACTIn this work we introduce an optimization–based method for the coupling of nonlocal and local diffusion problems. Our approach is formulated as a control problem where the states are the solutions of the nonlocal and local equations, the controls are the nonlocal volume constraint and the local boundary condition, and the objective of the optimization is a matching functional for the state variables in the intersection of the nonlocal and local domains. For finite element discretizations we present numerical results in a one–dimensional setting; though preliminary, our tests show the consistency and efficacy of the method, and provide the basis for realistic simulations.

Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains

We investigate interface problems in nonlocal diffusion and demonstrate how to reformulate and generalize the classical treatment of interface problems in the presence of nonlocal interactions. Through formal derivations, we show that nonlocal diffusion interface problems converge to their classical local counterparts, in the limit of vanishing nonlocality. A central focus of this paper is local/nonlocal interface problems, or interface problems with sharp transitions between local and nonlocal domains. Such problems can be cast as instances of a nonlocal interface problem, with a finite horizon in certain regions and a vanishing horizon in other regions. We derive a local/nonlocal interface problem and utilize conservation principles to obtain local/nonlocal interface conditions. Comparisons between nonlocal, local, and local/nonlocal interface problems are presented, analytically and numerically, with a focus on multiscale aspects of nonlocal models induced by their inherent length scales.

Krull dimension, overrings and semistar operations of an integral domain

In this paper, we will present new developments in the study of the links between the cardinality of the sets O ( R ) of all overrings of R, SSF c ( R ) of all semistar operations of finite character when finite to the Krull dimension of an integral domain R. In particular, we prove that if | SSF c ( R ) | = n + dim R , then R has at most n − 1 distinct maximal ideals. Moreover, R has exactly n − 1 maximal ideals if and only if n = 3 . In this case R is a Prüfer domain with exactly two maximal ideals and Y-graph spectrum. We also give a complete characterizations for local domains R such that | SSF c ( R ) | = 3 + dim R , and nonlocal domains R with | SSF c ( R ) | = | O ( R ) | = n + dim R for n = 4 , n = 5 , n = 6 and n = 7 . Examples to illustrate the scopes and limits of the results are constructed.

Mathematical methods for the study of nonlinear vibration problems

A symptotically valid mathematical results, based on the “Method of Averaging,” are given for nonlinear dynamical systems dependent on a parameter. Procedures are given for the study of transient and steady-state motions and for obtaining nonlocal domains of attraction of steady state motions of high-order nonlinear systems. The analysis is extended for the study of systems dependent on a “fast” and “slow” time, and connections of these systems to singularly perturbed systems are discussed.